A man wants to cut three lenghts from a single piece of board of length 91 cm . The secound length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?
[Hint : If x is length of the shortest board, then x, ( x+3) and 2x are the lengths of the second and third piece, respectively. Thus , `x + (x + 3 ) +3x le 91 and 2x ge (x + 3 ) + 5]`.

Answer

N/a

Explanation

Let the length of smallest board be x cm in the boards cut .
`:'` Length of second board = length of smallest board + 3
`rArr "Length of second board" = (x + 3) cm `
and length of third board = 2x cm
Now , x + (x + 3) + 2x `le` 91 (total length)
`rArr 4x + 3 le 91 `
`rArr 4x le 88`
`rArr x le 22" " ...(1)`
Given that, Length of third board - length of second board `ge 5 `
`rArr 2x - (x + 3 ) ge 5`
`rArr` x` ge` 8 ...(2)
From inequation (1) and (2) ,
`8 le x le 22`
`:.` Possible length of the smallest board will be between 8 cm and 22 cm.